University of GuilanJournal of Algebra and Related Topics2345-39319120210601Some classes of perfect annihilator-ideal graphs associated with commutative rings2129480510.22124/jart.2021.17227.1214ENM.AdlifardDepartment of Mathematics, Roudbar Branch Islamic Azad University, Roudbar, IranSh.PayroviDepartment of Mathematics, Imam Khomeini International University, Qazvin, IranJournal Article20200727Let $R$ be a commutative ring and let $\Bbb A(R)$ be<br />the set of all ideals of $R$ with nonzero annihilator.<br />The annihilator-ideal graph of $R$ is defined as the graph<br />${A_I}(R)$ with the vertex set $\Bbb A(R)^*=\Bbb A(R)\setminus\{0\}$ and two<br />distinct vertices $I$ and $J$ are adjacent if and only if<br />${\rm Ann}_R(IJ)\neq{\rm Ann}_R(I) \cup{\rm Ann}_R(J)$. In this paper, perfectness of<br />${A_I}(R)$ for some classes of rings is investigated.https://jart.guilan.ac.ir/article_4805_94dd66e60e677c95c058bec639a9936b.pdf